Problem: Simplify the following expression: $ z = \dfrac{-1}{10} - \dfrac{7p - 1}{3p + 4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3p + 4}{3p + 4}$ $ \dfrac{-1}{10} \times \dfrac{3p + 4}{3p + 4} = \dfrac{-3p - 4}{30p + 40} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{7p - 1}{3p + 4} \times \dfrac{10}{10} = \dfrac{70p - 10}{30p + 40} $ Therefore $ z = \dfrac{-3p - 4}{30p + 40} - \dfrac{70p - 10}{30p + 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-3p - 4 - (70p - 10) }{30p + 40} $ Distribute the negative sign: $z = \dfrac{-3p - 4 - 70p + 10}{30p + 40}$ $z = \dfrac{-73p + 6}{30p + 40}$